Question

Solve:

a.x3+x2-8x - 12x+2
b. x3-4x2-3x + 18x-3
c. x2 + 4x + 4
d. x2 - 6x + 9

Answer 1

Steps:

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

`((f)/(g))(x)=(x^2-x-6)/(1)/ (x-3)/(x+2)`

Next, remember that dividing by a number is the same as multiplying by its reciprocal. To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

`((f)/(g))(x)=(x^2-x-6)/(1)* (x+2)/(x-3)`

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

`((f)/(g))(x)=(x^2+2x-3x-6)/(1)* (x+2)/(x-3)`

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

`((f)/(g))(x)=(x(x+2)-3(x+2))/(1)* (x+2)/(x-3)`

Now you can rewrite it as:

`((f)/(g))(x)=((x-3)(x+2))/(1)* (x+2)/(x-3)`

Next, multiply:

`((f)/(g))(x)=((x-3)(x+2)^2)/(x-3)`

Next, divide:

`((f)/(g))(x)=(x+2)^2`

And lastly, simplify:

• A good tip:
  `(x+y)^2=x^2+2xy+y^2`

`((f)/(g))(x)=x^2+4x+4`

Answer:

The correct option is C. x² + 4x + 4.